Random signals and numbers have been used in various branches of science and technology, including, for example, statistical analysis, computer simulation [1], cryptography [2], gaming, and on-line casinos, among others. Random signals may be generally referred to as random numbers, however it should be understood that random signals may not be numbers, but random numbers may be based on random signals.
An example use of random numbers is in quantum key distribution (QKD) [3], where truly random numbers are desirable for both quantum state preparation and quantum state detection. Truly random numbers have also been desirable in testing fundamental principles of physics [4, 5].
In practice, it is not easy to obtain high quality random numbers with proven randomness [6]. The use of a weak random number may have undesirable results. For example, in a cryptographic system, the application of a weak random number generator (RNG) may be undesirable, as evidenced by Goldberg and Wagner's attack on the Netscape SSL implementation [7].
A conventional pseudorandom generator may generate a long train of “random” bits from a short random seed by employing deterministic algorithms. The generated long bit string could meet a number of statistical measures, which may allow it to pass most or all existing randomness tests. However, the entropy of the long bit string may be ultimately determined by the length of the random seed. Generally, random numbers generated by deterministic algorithms may not be truly random.
A physical RNG may generate random numbers from unpredictable physical processes, including, for example, thermal noise [9], radioactive decay [10], and air turbulence [11], among others. For example, the Intel 80802 Firmware Hub chip included a hardware random number generator [12]. It may be useful to distinguish between two different types of physical random number generation processes, based on the source of randomness: a process based on the chaotic behavior of classical deterministic systems, which may be referred to as type-one randomness; and a process based on the probabilistic nature of fundamental quantum processes [13], which may be referred to as type-two randomness. The term “classical noise” may be used to refer to the unpredictability of a deterministic chaotic system and the term “quantum noise” may be used to refer to the fundamental uncertainty in a quantum process.
For example, a RNG based on atmospheric conditions can be treated as a type-one RNG, since the randomness mainly may originate from the absence of enough information about the weather system. In other words, the observed fluctuation can be treated as classical noise. However, the weather change, while seemingly unpredictable in the eyes of a layman, may be predictable to an expert equipped with supercomputers.
Therefore, it may be desirable to provide a RNG based on quantum processes. Such a RNG may be useful in applications such as, for example, the generation of secure keys in a cryptographic system, or other secure exchange systems where the security relies on the true randomness of the key.